The Use of Deep Learning for Symbolic Integration: A Review of (Lample and Charton, 2019)

TL;DR

The paper investigates using a seq2seq transformer (LC) to learn symbolic integration and elementary ODE solving from a large synthetic corpus. It shows LC can outperform traditional systems on a specific, bias-prone test set when given substantial time, but highlights substantial limitations, including reliance on simplifiers, narrow problem scope (single-variable, elementary functions), and concerns about generalization. The authors argue that deep learning complements rather than replaces symbolic mathematics, and emphasize the dependence on high-quality symbolic components and carefully constructed benchmarks. Overall, the work demonstrates both the potential and the significant caveats of applying neural methods to symbolic reasoning tasks.

Abstract

Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are elementary functions. They found that, over a particular test set, the system could find solutions more successfully than sophisticated packages for symbolic mathematics such as Mathematica run with a long time-out. This is an impressive accomplishment, as far as it goes. However, the system can handle only a quite limited subset of the problems that Mathematica deals with, and the test set has significant built-in biases. Therefore the claim that this outperforms Mathematica on symbolic integration needs to be very much qualified.